The Research Of CDO Pricing Based On Factor Copula Model And Jump-diffusion Process

As a new development of credit derivatives,Collateralized Debt Obligation (CDO) based on credit of mortgage debt,through asset securitization technique,absorption of corporate bonds, bank loans and other asset to build asset pool,then redrawing investment risk and return to meet the different needs of investors. Drexel Burnham Lambert created the CDO product in 1987, Because of its mixture both asset securitization and credit derivatives product features and rapid development in the world. CDO becomes the most striking financial innovations in recent years.In this paper,the author firstly introduces the historical background and product features of the CDO,and review the basic model of CDO pricing. We comparison and analysis in the model's theoretical basis,assuming the rationality and efficiency of the computation and other aspects,respectively,demonstrated the traditional pricing models in China's CDO market adaptability. Combine research scholars of domestic and abroad to discuss the overall situation of China's financial market for the CDO pricing models.Secondly,we consider the CDO pricing problem when the time state is continuous; the risk-free interest rate is modeled by vasicek model and the asset values of reference entity respect to the jump-diffusion process. While,the volatility which including in the jump- diffusion process is the deterministic integrable function about the time .In the case of binary volatility,we calculate the characteristic function of cumulative loss of the reference entity's portfolio,with no-arbitrage pricing approach and the Fourier transform,the fair premium rates of the CDO tranches can be derived. Then,the case of binary volatility is extended to the case of multivariate volatility.Finally,we introduce the normal- NIG mixture distribution in Single-factor Copula model to discuss the CDO pricing problem. In this model,we establish two random correlation coefficient models, including the binary symmetric and the binary linear model. Respectively, calculate the characteristic function of cumulative loss of the reference entity's portfolio,with no-arbitrage pricing approach and the Fourier transform,we can get the fair premium rates of the CDO tranches. Then,we discuss the normal- NIG mixture distribution in Multi-factor Copula model, and also solve the problem of CDO pricing.Summary,in this paper,we consider the CDO pricing problem when the risk-free interest rate respect to vasicek model and the asset values of reference entity are modeled by the jump-diffusion process, this is a new idea in dynamic model research. Moreover,we introduce the normal- NIG mixture distribution in Single-factor and Multi-factor Copula model,and take into account fat tails factor Copula Structure and random correlation coefficient,Further improved the Copula factor pricing model.